Sigmoid Kernel

Mathematical and statistical functions for the Sigmoid kernel defined by the pdf, $$f(x) = 2/\pi(exp(x) + exp(-x))^{-1}$$ over the support \(x \in R\).

Details

The cdf and quantile functions are omitted as no closed form analytic expressions could be found, decorate with FunctionImputation for numeric results.

See also

Other kernels: Cosine, Epanechnikov, LogisticKernel, NormalKernel, Quartic, Silverman, TriangularKernel, Tricube, Triweight, UniformKernel

Super classes

distr6::Distribution -> distr6::Kernel -> Sigmoid

Public fields

name

Full name of distribution.

short_name

Short name of distribution for printing.

description

Brief description of the distribution.

Methods

Public methods

• Sigmoid$new()

• Sigmoid$pdfSquared2Norm()

• Sigmoid$variance()

• Sigmoid$clone()

Inherited methods

• distr6::Distribution$cdf()
• distr6::Distribution$confidence()
• distr6::Distribution$correlation()
• distr6::Distribution$getParameterValue()
• distr6::Distribution$iqr()
• distr6::Distribution$liesInSupport()
• distr6::Distribution$liesInType()
• distr6::Distribution$parameters()
• distr6::Distribution$pdf()
• distr6::Distribution$prec()
• distr6::Distribution$print()
• distr6::Distribution$quantile()
• distr6::Distribution$rand()
• distr6::Distribution$setParameterValue()
• distr6::Distribution$stdev()
• distr6::Distribution$strprint()
• distr6::Distribution$summary()
• distr6::Distribution$workingSupport()
• distr6::Kernel$cdfSquared2Norm()
• distr6::Kernel$mean()
• distr6::Kernel$median()
• distr6::Kernel$mode()
• distr6::Kernel$skewness()

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Method new()

Creates a new instance of this R6 class.

Usage

Sigmoid$new(decorators = NULL)

Arguments

decorators

(character())
Decorators to add to the distribution during construction.

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Method pdfSquared2Norm()

The squared 2-norm of the pdf is defined by $$\int_a^b (f_X(u))^2 du$$ where X is the Distribution, \(f_X\) is its pdf and \(a, b\) are the distribution support limits.

Usage

Sigmoid$pdfSquared2Norm(x = 0, upper = Inf)

Arguments

x

(numeric(1))
Amount to shift the result.

upper

(numeric(1))
Upper limit of the integral.

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Method variance()

The variance of a distribution is defined by the formula $$var_X = E[X^2] - E[X]^2$$ where \(E_X\) is the expectation of distribution X. If the distribution is multivariate the covariance matrix is returned.

Usage

Sigmoid$variance(...)

Arguments

...

Unused.

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Method clone()

The objects of this class are cloneable with this method.

Usage

Sigmoid$clone(deep = FALSE)

Arguments

deep

Whether to make a deep clone.